Spectral simulations of laminar-turbulent transition in plane Poiseuille flow and comparison with experiments
Laminar-turbulent transition in plane Poiseuille flow is simulated using the FourierChebyshev spectral method to integrate the three-dimensional time-dependent NavierStokes equations. For pressure computation, a new algorithm has been developed which enforces incompressibility and boundary conditions exactly even in the discretised equations. Detailed comparisons of the numerical results have been made with the vibrating-ribbon experiments of Nishioka et al. It is established that the numerical simulations reproduce the experimentally observed transition process up to the “spike” stage.
KeywordsSecondary Instability Oblique Wave Plane Poiseuille Flow Plane Channel Flow Chebyshev Spectral Method
Unable to display preview. Download preview PDF.
- M. Nishioka, S. Iida, Y. Ichikawa: An experimental investigation of the stability of plane Poiseuille flow. J.Fluid Mech. 72 (1975) 731–751Google Scholar
- M. Nishioka, S. Iida, S. Kanbayashi: An experimental investigation of the subcritical instability in plane Poiseuille flow (in Japanese). Proc. 10th Turbulence Symposium, Inst. Space Aeron. Sci., Tokyo Univ., 1978, p. 55-62Google Scholar
- M. Nishioka, M. Asai, S. Iida: An experimental investigation of the secondary instability. Proc. IUTAM Symposium, Stuttgart, 1979 (ed. R. Eppler, H. Fasel) Springer, Berlin 1980, 37–46Google Scholar
- Th. Herbert: Stability of plane Poiseuille flow-theory and experiment. Report VPI-E-81-35, to be published in Fluid Dynamics TransactionsGoogle Scholar
- S.A. Orszag, L.C. Kells: Transition to turbulence in plane Poiseuille and plane Couette flow. J.Fluid Mech. 96 (1980) 159–205Google Scholar
- S.A. Orszag, A.T. Patera: Subcritical transition to turbulence in plane channel flows. Phys.Rev.Lett. 45 (1980) 989–993Google Scholar
- L. Kleiser: Numerische Simulationen zum laminar-turbulenten Umschlagsproze\ der ebenen Poiseuille-Str6mung. Dissertation, Karlsruhe 1982 (report KfK3271)Google Scholar
- L. Kleiser, U. Schumann: Treatment of incompressibility and boundary conditions in 3-D numerical spectral simulations of plane channel flows. Proc. 3rd GAMM-Conference on Numerical Methods in Fluid Mechanics (ed. E.H. Hirschel), Vieweg Verlag, Braunschweig 1980, 165–173Google Scholar
- D. Gottlieb, S.A. Orszag: Numerical analysis of spectral methods: Theory and applications. NSF-CBMS Monograph 26, SIAM, Philadelphia 1977Google Scholar